A QUEUEING-THEORETICAL FRAMEWORK FOR QOS-ENHANCED SPECTRUM MANAGEMENT IN COGNITIVE RADIO NETWORKS

Completion of primary connections λp(2) H p( 3 )_λ s S Interrupt f_p(1)_(x) f_i(1)_(φ)

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Cognitive radio (CR) allows low-priority sec-ondary users to temporarily utilize the unused licensed channel of high-priority primary users, thereby significantly improving overall spec-trum efficiency [1]. However, the secondary users need to vacate the occupied channel when the primary users appear. In order to

return the occupied channel to the primary user and discover a suitable target channel to resume the unfinished transmission, spectrum

handoff procedures are initiated for the

sec-ondary users.1_{Basically, according to the} prin-ciple of selecting the target channel for spectrum handoff, the operating modes of the secondary networks can be categorized as non-hopping and non-hopping. In the non-non-hopping mode, the secondary user always stays on its current operating channel when it is interrupt-ed, which is the basic mode of IEEE 802.22 systems [3]. In the hopping mode, the inter-rupted secondary user can stay on its current operating channel or change to another chan-nel according to traffic statistics. An example of the hopping mode is the phase-shifting hop-ping method used in IEEE 802.22 systems [3]. Secondary users’ connections may execute mul-tiple handoffs during its transmission period due to interruptions from primary users [4]. Clearly, these handoffs will degrade the quality of service (QoS) performance of the secondary users in providing sensitive traffic.

In order to overcome the performance degra-dation due to multiple spectrum handoffs in the non-hopping or hopping mode, various spectrum management techniques are re-examined from the perspective of link connection quality for the secondary users. The spectrum management techniques include:

• Spectrum sensing (detecting an unused chan-nel in the sensing phase)

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BSTRACT

This article outlines the fundamental model-ing issues of opportunistic spectrum access in cognitive radio networks. In particular, we iden-tify the effects of connection-based channel usage on the QoS performance of spectrum management techniques. During the transmis-sion period of a secondary user’s connection, the phenomenon of multiple spectrum handoffs due to interruptions of primary users arises quite often. In addition to multiple interruptions, the connection-based channel usage behaviors are also affected by spectrum sensing time, switching between different channels, generally distributed service time, and channel contention between multiple secondary users. An analytical frame-work based on the preemptive resumption prior-ity M/G/1 queueing theory is introduced to characterize the effects of the above factors simultaneously. The proposed generalized ana-lytical framework can incorporate various system parameters into the design of very broad trum management techniques, including spec-trum sensing, specspec-trum decision, specspec-trum sharing, and spectrum mobility. The applications of this analytical framework on spectrum deci-sion as well as spectrum mobility are discussed, and some open issues using this framework are suggested in this article.

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This work was presented in part at the IEEE International Performance Computing and Communications Confer-ence (IPCCC), 2008. This work was supported in part by the MoE ATU Plan and the National Science Council (NSC) grant 97-2917-I-009-109.

1_{Spectrum handoff in CR networks is different from the} conventional handoff mechanisms in cellular mobile net-works. Spectrum handoff considers two types of users with different priorities, where the high-priority primary users have the right to interrupt the transmission of the low-pri-ority secondary users. When the interruption event occurs, the secondary user must stop using the current channel even though the received signal strength is still acceptable. In contrast, all users in the conventional handoff mecha-nisms have the same priority to access channels, and they change their operating channels mainly due to deteriora-tion of signal quality [2].

The authors outline

the fundamental

modeling issues of

opportunistic

spectrum access in

cognitive radio

networks. They

identify the effects

of connection-based

channel usage on

the QoS performance

of spectrum

manage-ment techniques.

• Spectrum decision (selecting the best initial channel in the analysis phase)

• Spectrum sharing (avoiding collision in the access phase)

• Spectrum mobility (switching to a suitable channel when a licensed primary user appears) Referring to [5], the relationships of these four spectrum management functionalities are shown in Fig. 1. In the figure, the secondary users first request channels from the CR network. With the spectrum decision functionality, they can deter-mine their initial operating channels from all M candidate channels based on the spectrum sens-ing outcomes. The spectrum sharsens-ing functionali-ty must be implemented to alleviative channel contention when multiple secondary users access the same channel. Furthermore, if a primary user appears on the occupied channel, the spec-trum handoff procedures in the specspec-trum mobili-ty functionalimobili-ty must be initiated.

In this article, in order to evaluate the QoS performance of spectrum management tech-niques in the hopping mode, an analytical frame-work based on the preemptive resumption priority (PRP) M/G/1 queueing theory is devel-oped. The proposed analytical framework can provide important insights into the design of the system parameters of spectrum management techniques for various traffic arrival rates and service time distributions. The effectiveness of the proposed analytical framework is illustrated by some examples. Specifically, we investigate how to design a load balancing spectrum deci-sion scheme and evaluate the latency perfor-mance of various spectrum handoff schemes based on the proposed analytical framework. In conclusion, the transmission latency of secondary users can be improved significantly if they can adaptively adopt the optimal system parameters according to traffic conditions. Finally, we sug-gest some open issues on top of the proposed analytical model.

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An important issue for a CR network is to devel-op an analytical framework to characterize the behaviors of the connection-based channel usage, including:

• Multiple interruptions and handoffs • Spectrum sensing time

• Various operating channels • Generally distributed service time

• Channel waiting time due to multiple sec-ondary users

Many analytical models have been proposed to characterize these features [6–9]. However, these five key design features have not been consid-ered simultaneously.

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As shown in Table 1, the current modeling tech-niques of channel usage behaviors in CR net-works can be classified into three categories: the partially observable Markov decision process (POMDP), the two-dimensional Markov chain, and the PRP M/G/1 queueing model.

In [6], the evolution of the channel usage of

the primary network is characterized by a dis-crete-time Markov chain that has two occupancy states (busy and idle). The framework of POMDP was developed to preselect the best action (target channel) to maximize the immedi-ate reward (expected per-slot throughput) of the decision maker (secondary user) at the next time slot [6]. In addition to the effects of the traffic loads of the primary network, the effects of the traffic loads of both the primary and secondary users on the statistics of channel occupancy were considered in [7], where a two-dimensional Markov chain is used to represent the total num-bers of primary and secondary users in a CR network, respectively. When the secondary users are interrupted, it is assumed that they can immediately find an idle channel if at least one idle channel exists. As a result, the spectrum sensing time is neglected in this model. Further-more, the Markov chain model is more suitable for exponentially distributed service time. It is unclear how to extend this kind of model to the case with generally distributed service time.

Some researchers have used the PRP M/G/1 queueing model to characterize the spectrum usage behaviors of each channel. Based on this model, the effects of multi-user contention and multiple interruptions on the latency perfor-mance of secondary users’ connections were studied in [8, 9]. However, this PRP M/G/1 queueing model considered the non-hopping mode; thus, there is only one candidate channel for spectrum handoff. Note that the sensing time issue is not addressed in this model.

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Compared to the traditional PRP M/G/1 queue-ing model, the proposed PRP M/G/1 queuequeue-ing network model resolves two new challenging conditions:

• Various operating channels in the hopping model

• Spectrum sensing time

Figure 1. Relationships between spectrum sensing, spectrum decision, spectrum sharing, and spectrum mobility functionalities.

Spectrum decision Arrivals of secondary users Channel 1 Channel 2 Channel M Spectrum handoff Spectrum mobility Spectrum sharing Spectrum sensing

First, it is challenging to find a unifying model to characterize the channel switching behaviors for various target channel selection methods. We provide a systematic approach based on the pro-posed PRP M/G/1 queueing network model to catch the randomness property of the target channel selection, and evaluate its effects on the system performance metrics of transmission latency and channel utilization. Second, in the hopping mode secondary users may need to per-form spectrum sensing to search for idle chan-nels. The suggested PRP M/G/1 queueing network can also easily incorporate the sensing time into performance analysis.

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Figure 2 illustrates the transmission processes of a secondary connection in a two-channel CR net-work. The procedures consist of the following steps: •In Fig. 2a, a secondary user plans to estab-lish a new connection flow SCAto its intended

receiver.

•Next, in Fig. 2b, the transmitter and receiver decide on their initial operating channel for SCA.

In this example, they can select channel Ch1 or Ch2.

•In Fig. 2c, SCAis established at Ch1. During

the transmission period of SCA, a request from a

primary connection may arrive at Ch1.

•Next, in Fig. 2d, SCAdetects the appearance

of a primary user.2_{Then the spectrum handoff} procedures are initiated to vacate Ch1 and dis-cover a suitable target channel to resume the unfinished transmission.

•In Fig. 2e, the target channel of SCAis

decided for spectrum handoff. If the non-hop-ping mode is adopted, the operating channel of SCAcannot be changed; thus, SCAmust select

Ch1 to be its target channel. However, SCAcan

select Ch1 or Ch2 for its target channel when the hopping mode is adopted. There are many methods of selecting the target channel. For example, the target channel can be searched for by instantaneous spectrum sensing at this moment of interruption. In this case, the effect of spectrum sensing time τ on the latency perfor-mance of SCAmust be considered.

•Finally, if SCAchooses to stay on Ch1, its

remaining transmission will be resumed after all traffic loads of the primary users at Ch1 have been served, as shown in Fig. 2f. On the other hand, if the decision is to change to Ch2, there are two possible situations. If Ch2 is idle, SCA

can transmit remaining data immediately as shown in Fig. 2g. Otherwise, SCAmust wait at

the queue until all secondary users in the pre-sent queue of Ch2 are served, as shown in Fig. 2h.

•Note that similar spectrum handoff behav-iors may be executed many times because a sec-ondary user’s connection may experience multiple interruptions from primary users during its transmission period. Hence, the procedures from Figs. 2c–2h will be executed repeatedly. In this article, a set of target channels, called the

target channel sequence, will be selected

sequen-tially.

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Now we propose a preemptive resume priority (PRP) M/G/1 queueing network model to char-acterize the connection-based spectrum usage behaviors in CR networks. This model is very general and can easily be adjusted to evaluate the performance of various spectrum manage-ment techniques under different traffic condi-tions. Furthermore, it can also be applied to general CR network architectures, including ad hoc and centralized CR networks. Key features of the proposed queueing network model are listed below:

•Each server (channel) has two types of cus-tomers (connections). Before transmitting data, the traffic of the primary and secondary users enter the high-priority and low-priority queues,3 respectively. According to the traffic arrival time at queues, the primary and secondary

con-nections can be established without any

colli-sions. The first come first served (FCFS) scheduling discipline is adopted to arrange the transmission order for these connections with the same priority.4

2 _{We assume that the} con-sidered CR network is a time-slotted system. In order to detect the pres-ence of primary users, each secondary user must perform spectrum sensing at the beginning of each time slot. If the current operating channel is idle, the secondary user can transmit one slot-sized frame in this time slot. Otherwise, the secondary user must perform spec-trum handoff procedures to resume its unfinished transmission on the target channel. Furthermore, the secondary user can differ-entiate the appearance of a primary user or sec-ondary user by existing spectrum sensing tech-niques such as feature detection. The issue of dif-ferentiating primary and secondary users is beyond the scope of this article. 3_{Note that we assume the} considered two queues to have infinite length. 4_{In fact, the analytical} results of mean values obtained from the pro-posed framework can be applied to another scheduling discipline that is independent of the ser-vice time of the primary and secondary connec-tions because the averages of system performance metrics will be invariant to the order of service in this case [10, p. 113].

Table 1. Comparison of various analytical models for CR Networks, where the signs “” and “×” indicate that the proposed model “does” and “does not” consider the corresponding feature, respectively.

Model Name Multiple

spectrum handoffs Spectrum sensing time Various operating channels General service time Multiple secondary connections POMDP [6] _ × _ × × Two-dimensional Markov chain [7]  ×  ×  PRP M/G/1 queuing model [8, 9]  × ×   Proposed RPR M/G/1

•Primary users have the preemptive priority to interrupt the transmissions of secondary users. Interrupted secondary users can resume the unfinished transmission on the selected target channel instead of all the data.

•A secondary connection may experience multiple interruptions from primary users during its transmission period.

Note that this model can be also extended to characterize the effects of heterogeneous chan-nel bandwidth [11]. Some assumptions are adopt-ed for ease of analysis.

• The arrival processes of the primary and sec-ondary connections are Poisson.

• Only one user can transmit on each channel at any time instant.

• The secondary transmitter can notify its corre-sponding receiver with the interruption event according to spectrum handoff protocols [12].

Figure 3 shows an example of the PRP M/G/1 queueing network model with three channels.

Let λsbe the arrival rate of the secondary

con-nections in a CR network. When a secondary connection arrives at the CR network, it can select its initial operating channel. Let p(k)_be the probability of selecting channel k. Thus, the effective arrival rate of the secondary connection at channel k is λs(k)= p(k)λs. Note that various

spectrum decision algorithms will result in differ-ent values of p(k)_.

When a newly arriving secondary user’s data is connected to the low-priority queue of its idle initial operating channel, it can be transmitted immediately. If a primary connection appears at channel k, a secondary connection using channel

k will be interrupted. In this case, the secondary

connection can decide to stay on the current operating channel or change to another channel through different feedback paths, depending on the operating mode and the adopted spectrum handoff scheme. If choosing to stay on its current operating channel, the interrupted secondary

Figure 2. Illustration of transmission procedures in a two-channel system. The medium green areas indicate that the channels are occu-pied by existing primary users’ connections (PCs) or other secondary users’ connections (SCs): a) the transmitter of the secondary con-nection SC_Aplans to establish a connection flow to the intend receiver; b) the transmitter and receiver of SC_Acan select channel Ch1 or Ch2 as the initial operating channel; c) during the transmission period of SC_A, a primary connection arrives at Ch1; d) the transmis-sion of SC_Ais stopped; e) the target channel of SC_Ais decided for spectrum handoff, they can either stay on Ch1 or change to Ch2; f) SC_Avacates Ch1 and then resumes the unfinished transmission when Ch1 becomes idle; g) SC_Avacates Ch1 and changes its operating channel to the idle channel, Ch2; h) SC_Avacates Ch1 and changes its operating channel to the busy channel, Ch2.

Ch1 SC_A Ch2 PCs or SCs Ch1

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SC_A stops its current transmission Ch1 Ch2 PCs or SCs (f) (e) Ch1 Ch2 PCs or SCs Choice 2: change

Choice 1: stay Choice 1: stay

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Choice 2: change Choice 2: change

SC_A SC_A SC_A SC_A SC_A is resumed at Ch2 Ch1 Ch2 PCs or SCs PCs or SCs

connection places the remaining data and wait at the head of the low-priority queue of the current operating channel. If it decides to change its operating channel, its remaining data will be con-nected to the tail of the low-priority queue of another channel. Note that ⊕ indicates that the traffic loads of the interrupted secondary connec-tions are merged. When the interrupted sec-ondary connection transmits its remaining data on the selected target channel, it might be inter-rupted again. Hence, the proposed model can describe the effects of multiple handoffs.

In Fig. 3, represents the channel selection point, where the newly arriving secondary con-nection must select its initial operating channel, or the interrupted secondary connection must select its target channel for spectrum handoff. There are many methods to select these chan-nels. For example, the secondary connection can decide its initial operating channel or target channel according to the predetermined proba-bility or the outcomes from instantaneous spec-trum sensing. If the specspec-trum sensing is executed to search the idle channels, can be regarded as a tapped delay line or a server with constant service time, which is related to sensing time. Hence, the effects of spectrum sensing time on the latency performance of secondary connec-tions can be characterized.

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Now, we explain why the proposed model can characterize the connection-based channel usage behaviors of a CR network. In order to accurate-ly characterize the transmission processes of a

secondary connection, we must take the seven events discussed earlier into account.

•Secondary connection arrival event (Fig. 2a): We assume that the arrival process of the secondary connections is Poisson. Let Xsand fs(x) be the service time of the secondary

con-nections and its probability density function (PDF), respectively.

•Initial channel selection event of the sec-ondary connections (Fig. 2b): We use p(k)_to rep-resent the probability that the secondary connection selects channel k for its initial operat-ing channel. Furthermore, if spectrum sensoperat-ing is executed to decide the initial operating channel, the effect of sensing time can be modeled by .

•Primary connection arrival event (Fig. 2c): We assume that the arrival process of the prima-ry connection is Poisson. Denoteby λ(k)p the

arrival rate of the primary connections with default channel k. Furthermore, let X(k)p and f(k)p (x) be the service time of the primary

connec-tion at channel k and its corresponding PDF. •Interruption event (Fig. 2d): In the PRP M/G/1 queueing network model, the primary users have the preemptive priority and can inter-rupt the secondary user’s transmission. In other words, the secondary users must vacate the occu-pied channel when the primary users appear.

•Target channel selection event (Fig. 2e): An interrupted secondary connection can stay on its current channel or change to another channel. To this end, its remaining transmission must be connected to the low-priority queue of the cur-rent channel or another channel through differ-ent feedback paths. Furthermore, if the spectrum sensing is executed to search the target channel, the effects of sensing time can be modeled by S.

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Figure 3. The PRP M/G/1 queueing network model with three channels. λp(k), λs(k), and ωn(k)are the arrival rates of the primary

connec-tions, the secondary connecconnec-tions, and the type-n secondary connections (n ≥ 1) at channel k. Note that ω0(k)= λs(k). Furthermore, fp(k)(x) and fi(k)(φ) are the PDFs of Xp(k)and Φi(k), respectively.

λp(3) _{Channel 3} High-priority queue Low-priority queue Completion of primary connections Completion of secondary connections Completion of secondary connections Completion of primary connections Completion of primary connections S λs ( w i t h f_s(_χ)) Interrupt f_p(3)(x) p( 3 )_λ s ωn(3) λp(2) _{Channel 2} High-priority queue Low-priority queue Interrupt f_p(2)(x) f_i(2)_(φ) p( 3 )_λ s ωn(2) λp(1) _{Channel 1} High-priority queue Low-priority queue Completion of secondary connections S Interrupt f_p(1)(x) f_i(1)_(φ) p( 1 )_λ s ωn(1) S S f_i(3)_(φ)

•Resumption event (Figs. 2f–h): The inter-rupted secondary connection can resume its unfinished transmission on the target channel instead of retransmitting all of the data.

•Multiple handoff events: Two auxiliary parameters (ωi(k)and Φi(k)) are suggested to

char-acterize the traffic flows of interrupted sec-ondary connections.

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In Fig. 3, we use two auxiliary parameters to characterize the traffic flows of the interrupted secondary connections. Type-i secondary connec-tions represent secondary connecconnec-tions that have experienced i interruptions. Denote ω(k)i as the

arrival rate of traffic flows redirected from the type-(i – 1) secondary connections at channel k. That is, ωi(k)is the arrival rate of the type-i

sec-ondary connections at channel k. Note that ω0(k)= λs(k). Furthermore, let Φi(k)be the

trans-mission duration of a secondary connection between the ith and the (i+1)th_{interruptions at}

channel k and fi(k)(Φ) be the PDF of Φi(k). That

is, Φi(k)is the effective service time of the type-i

secondary connections at channel k.

Figure 4 illustrates the physical meaning of random variable Φi(k). Recall that Xsis the service

time of the secondary connections. We generate

Xsfive times in Fig. 4, where the five realizations

are divided into many segments due to multiple primary users’ interruptions. For example, the first secondary connection (realization) is divided into four segments because it experiences three interruptions at channels 1, 1, 1, and 2, respec-tively. Thus, this secondary connection’s initial operating channel is Ch1, and its target channel sequence is (Ch1, Ch1, Ch2). In Fig. 4, random variable Φ(1)₂ is one of the darker regions, repre-senting the transmission duration of a secondary connection between the second and third inter-ruptions at Ch1. That is, Φ(1)₂ is one of the third segments of the first, third, and fourth secondary connections in Fig. 4. Note that the fifth sec-ondary connection in Fig. 4 does not have a third segment because it is interrupted only once.

In the hopping mode, it is quite complex to find the PDF of the effective service time of each segment because the effective service time is dependent on the traffic statistics of the pri-mary and other secondary users of each channel, and the operating channels for these segments can be different. Based on the proposed analyti-cal framework, we provide a systematic approach to evaluate the impacts of various system

param-Figure 4. Illustration of the physical meaning of random variable Φi(k). For example, Φ2(1)is one of the third segments (darker areas) of the first, third, and fourth secondary connections.

3rd 2nd 1st 3rd 2nd 1st 3rd 2nd 1st 4th φ0(2) 1st 2nd 1st X_s Interruption event occurs #1 on Ch1 #2 on Ch1 #3 on Ch1 #4 on Ch1 φ0(1) φ1(1) φ2(1) φ3(2) #1 on Ch1 #2 on Ch2 #3 on Ch1 #4 on Ch1 φ0(1) φ1(2) φ2(1) φ3(1) #1 on Ch2 #2 on Ch1 #3 on Ch1 #4 on Ch2 φ0(2) φ1(1) φ2(1) φ3(2) #5 on Ch1 φ4(1) #1 on Ch2 #2 on Ch2 φ1(2) #1 on Ch2 #2 on Ch1 #3 on Ch2 φ0(2) φ1(1) φ2(2)

When the interrupted

secondary connection

transmits its

remaining data on

the selected target

channel, it is

possible to be

interrupted again.

Hence, the proposed

model can describe

the effects of

multiple handoffs.

eters on the effective service time and can help derive the closed-form expression for the PDF of the effective service time of each segment.

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Finally, we denote ρ(k)_{as the busy probability of} channel k. In an M-channel network, the follow-ing constraint shall be satisfied:

(1) where ρ(k)_{can be also interpreted as the} utiliza-tion factor of channel k.

In the following, we provide two examples to illustrate the effectiveness of the proposed ana-lytical framework. Specifically, we focus on designing the load balancing spectrum decision scheme and the evaluation of latency perfor-mance for various spectrum handoff schemes.

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Spectrum decision helps the secondary user select the best initial channel to transmit data. In order to evenly distribute the traffic loads of sec-ondary users to candidate channels, an effective spectrum decision scheme should take into account not only the traffic statistics of the pri-mary and secondary users, but also interruptions from the primary users.

Here, we focus on the probability-based chan-nel selection scheme, where the secondary user selects its initial operating channel from M can-didate channels based on the predetermined dis-tribution probability vector (denoted by p = (p(1)_{, p}(2)_{, º, p}(M)_{)). Obviously, this scheme must} consider the load balancing issues and prevent the secondary connections from selecting a busy channel. Hence, it is important to determine the optimal channel selection probability to mini-mize the transmission latency of the secondary connections. To this end, we formulate an opti-mization problem to find the optimal distribu-tion probability vector (denoted by p*) to minimize the average overall system time of the secondary connections (denoted by E[S]), which is defined as the duration from the instant data arrive at the system until the instant the whole transmission is finished. Specifically,

(2) The closed-form expression for E[S] was derived in [11] based on the proposed model. Hence, p* can be determined easily.

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Target channel selection in spectrum mobility functionality is an important problem. Unlike the traditional PRP M/G/1 queueing model con-sidering only the non-hopping mode, we further consider the hopping mode in our proposed PRP M/G/1 queueing network model. According to the decision timing for selecting target chan-nels, handoff mechanisms in the hopping mode can be categorized into proactive and reactive handoff schemes [13, 14]. The proactive handoff scheme proactively determines the target channel

sequence before data transmission. In this case, it is necessary to resolve the issue of channel obso-lescence because the preselected target channel may not be available when the handoff is requested. Because the channel obsolescence issue will increase the extended data delivery time, the key challenge is to predetermine the optimal target channels to minimize the extend-ed data delivery time, especially in the case of multiple handoffs. Here, the extended data delivery time of a secondary connection is defined as the duration from the instant of trans-mitting data until the instant of finishing the whole transmission. On the other hand, for the reactive handoff scheme, the target channel is searched for by reactively spectrum sensing after handoff request is initiated. Then the secondary users can resume the unfinished transmission on one of the idle channels. Hence, the target chan-nel sequence is a random sequence depending on the traffic statistics and sensing outcomes. In this case, spectrum sensing time is a key domi-nant factor for the extended data delivery time.

Both proactive and reactive handoff schemes have their own advantages and disadvantages. The reactive handoff scheme can reduce its extended data delivery time by avoiding selecting a busy channel, but at the cost of relying on fast spectrum sensing techniques. The proactive handoff can save the time of scanning the whole spectrum to determine the target channel, but the predetermined target channel may not be available when it is requested by the secondary user. Thus, an interesting open problem is to determine which spectrum handoff scheme can result in the shortest extended data delivery time under various traffic parameters and sensing times [13, 14].

Figure 5 compares the extended data delivery time for the proactive and reactive handoff schemes. Here, we consider a two-channel sys-tem with the following traffic parameters: λ(1)s =

λ(2)s = 0.01, E[Xp(1)] = E[Xp(2)] = 10, and λp(2)=

λp(2)= λp. From this figure, we have the

follow-ing important observations. First, the extended data delivery time of the reactive handoff has a singular point at λp= 0.043. This is because the

two different predetermined target channel sequences are adopted in the cases of λp< 0.043

and λp> 0.043. Based on the proposed model,

the traffic-adaptive proactive handoff scheme can be designed to appropriately change to a better target channel sequence according to traf-fic conditions. Next, we focus on the reactive handoff scheme. In the ideal case where spec-trum sensing time (denoted by τ) is 0, the extended data delivery time can be shortened around 7~20 percent compared to the proactive handoff scheme over various arrival rates of the primary connections. This is because the reactive handoff scheme can perform spectrum sensing to find the idle channels immediately. When τ = 5, the reactive handoff scheme is not always bet-ter than the proactive handoff scheme. Specifi-cally, when λp< 0.037, the proactive handoff

scheme can result in shorter extended data deliv-ery time. Hence, we can conclude that the proac-tive handoff scheme yields shorter extended data delivery time than the reactive handoff scheme when the traffic loads of the primary users are

p p p * arg min=

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An interesting open

problem is to

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sensing time.

light, whereas the reactive scheme performs bet-ter with heavy traffic loads. Finally, the reactive handoff scheme will result in the longest extend-ed data delivery time when τ = 10. Basextend-ed on the proposed model, a principle to determine which handoff scheme should be adopted in CR net-works can be designed for various sensing times and traffic parameters.

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The proposed queueing network model provides a systematic method to help the design of spec-trum management technologies. It can catch the five general behaviors for connection-based channel usage. More applications have been dis-cussed in [11, 13–15]. Some interesting research issues that can be extended from the proposed model include the following:

•An important research direction of spectrum

sensing is to consider the effects of missed

detec-tion and false alarm on the latency performance of primary and secondary users. These two kinds of sensing errors lead to the extension of the overall system time of primary and secondary connections. Preliminary results using the pro-posed analytical model with imperfect sensing can be found in [11].

•From the viewpoint of spectrum decision, it is worthwhile to determine the optimal distribu-tion probability vector for the probability-based spectrum decision method when secondary con-nections may have different opinions on the observed traffic statistics λ(k)p , λs, fp(k)(x), and fs(x).

•An interesting spectrum sharing issue is to incorporate the distributed channel contention behaviors into the proposed model. In the pro-posed model, we assume that the FCFS schedul-ing policy is adopted. For a distributed medium access control (MAC) protocol such as carrier sense multiple access (CSMA), the channel con-tention time and retransmission in the MAC layer should be taken into account when calcu-lating the latency performance of secondary users. Furthermore, the proposed queueing net-work model can facilitate the design of an inter-ference-avoiding admission control mechanism, discussed briefly in [15].

•The proposed model assumes that the

spec-trum mobility functionality can help an

interrupt-ed secondary user resume its unfinishinterrupt-ed data transmission on a suitable channel. This resump-tion policy can be characterized by the preemp-tive resumption priority queueing network. However, in other scenarios, an interrupted sec-ondary user may need to retransmit the whole connection rather than resuming the unfinished transmission. In this situation, a CR network should be modeled by the preemptive repeat pri-ority queueing network. It is also worthwhile to investigate the latency performance results from different transmission policies.

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ONCLUSIONS

In this article, the preemptive resume priority (PRP) M/G/1 queueing network model has been proposed to evaluate the QoS performance of various spectrum management techniques in the

non-hopping and hopping modes. This analytical framework can characterize the general behavior of connection-based channel usage and help evaluate QoS performance in various traffic con-ditions. In order to demonstrate the effective-ness of this model, we present two examples to explain how to design system parameters for the probability-based spectrum decision schemes and evaluate the latency performance of different spectrum handoff schemes. There are still many open problems for spectrum management tech-niques. On top of the proposed analytical frame-work, it is expected that better traffic-adaptive solutions can be provided to solve these open issues from a systematic viewpoint.

R

EFERENCES

[1] I. F. Akyildiz et al., “A Survey on Spectrum Management in Cognitive Radio Networks,” IEEE Commun. Mag., vol. 46, no. 4, pp. 40–48, Apr. 2008.

[2] A. Sgora and D. D. Vergados, “Handoff Prioritization and Decision Schemes in Wireless Cellular Networks: A Survey,” IEEE Commun. Surveys and Tutorials, vol. 11, no. 4, 2009, pp. 57–77.

[3] W. Hu et al., “Dynamic Frequency Hopping Communi-ties for Efficient IEEE 802.22 Operation,” IEEE Commun.

Mag., vol. 45, no. 5, May 2007, pp. 80–87.

[4] H.-J. Liu et al., “Study on the Performance of Spectrum Mobility in Cognitive Wireless Network,” IEEE Singapore

Int’l. Conf. Commun. Sys., June 2008.

[5] C.-W. Wang, Queueing-Theoretical Spectrum

Manage-ment Techniques for Cognitive Radio Networks, Ph.D.

dissertation, Nat’l. Chiao-Tung Univ., Sept. 2010. [6] Q. Zhao and A. Swami, “A Decision-theoretic

Frame-work for Opportunistic Spectrum Access,” IEEE Wireless

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[7] X. Zhu, L. Shen, and T.-S. P. Yum, “Analysis of Cognitive Radio Spectrum Access with Optimal Channel Reserva-tion,” IEEE Commun. Letters, vol. 11, no. 4, Apr. 2007, pp. 304–06.

[8] C. Zhang, X. Wang, and J. Li, “Cooperative Cognitive Radio with Priority Queueing Analysis,” IEEE ICC ’09, June 2009.

[9] P. Zhu, J. Li, and X. Wang, “Scheduling Model for Cog-nitive Radio,” Int’l. Conf. CogCog-nitive Radio Oriented

Wireless Networks and Commun., May 2008.

[10] L. Kleinrock, Queueing Systems — Volume 2:

Comput-er Applications, Wiley, 1975.

Figure 5. Comparison of the average extended data delivery time for different spectrum handoff schemes, where E[Xs] = 10.

Arrival rate of the primary connections (λp) 0.035

0.03 12 10 Average extended data delivery time 14 16 18 20 22 24 26 28 0.04 0.045 0.05 0.055 0.06 Proactive handoff scheme

Reactive handoff scheme (τ = 10) Reactive handoff scheme (τ = 5) Reactive handoff scheme (τ = 0)

[11] L.-C. Wang, C.-W. Wang, and F. Adachi, “Load-Balanc-ing Spectrum Decision for Cognitive Radio Networks,”

IEEE JSAC, vol. 29, no. 4, Apr. 2011, pp. 757–69.

[12] X. Liu and Z. Ding, “ESCAPE: A Channel Evacuation Protocol for Spectrum-agile Networks,” IEEE DySPAN, Apr. 2007.

[13] L.-C. Wang, C.-W. Wang, and C.-J. Chang, “Modeling and Analysis for Spectrum Handoffs in Cognitive Radio Networks,” IEEE Trans. Mobile Computing, 2011. [14] C.-W. Wang, L.-C. Wang, and F. Adachi, “Modeling

and Analysis for Reactive-Decision Spectrum Handoff in Cognitive Radio Networks,” IEEE GLOBECOM ’10, Dec. 2010.

[15] —, “Optimal Admission Control in Cognitive Radio Networks with Sensing Errors,” IEICE tech. rep., vol. 109, no. 440, Mar. 2010, pp. 491–96.

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LI-CHUNWANG[M’96, SM’06, F’11] (lichun@cc.nctu.edu.tw) received his B.S. degree from National Chiao Tung Universi-ty, Taiwan, R.O.C., in 1986, his M.S. degree from National Taiwan University in 1988, and M.S. and Ph. D. degrees from Georgia Institute of Technology, Atlanta, in 1995 and 1996, respectively, all in electrical engineering. From 1996 to 2000 he was with AT&T Laboratories, where he was a senior technical staff member in the Wireless Communica-tions Research Department. Since August 2000 he has been an associate professor in the Department of Commu-nication Engineering of National Chiao Tung University, Taiwan. He was a co-recipient (with Gordon L. Stüber and Chin-Tau Lea) of the 1997 IEEE Jack Neubauer Best Paper Award. He has published over 150 journal and internation-al conference papers. He was elected an IEEE Fellow in 2011 for his contributions in cellular architectures and radio resource management in wireless networks. He served as an Associate Editor for IEEE Transactions on

Wireless Communications from 2001 to 2005, and as

Guest Editor of Special Issues, on Mobile Computing and Networking for IEEE Journal on Selected Areas in

Commu-nications in 2005 and on Radio Resource Management and

Protocol Engineering in Future IEEE Broadband Networks

for IEEE Wireless Communications in 2006. He has eight U.S. patents.

CHUNG-WEIWANG[S’07] (hyper.cm91g@nctu.edu.tw) received his B.S. degree in electrical engineering from Tamkang University, Taipei, Taiwan, in 2003, and M.S. and Ph.D. degrees in applied mathematics and communication engineering from National Chiao Tung University in 2007 and 2010, respectively. From 2009 to 2010 he was also a visiting scholar at Tohoku University, Sendai, Japan. He was awarded student travel grants for IEEE ICC ’09 and GLOBE-COM ’10. His current research interests include cross-layer optimization, MAC protocol design, and radio resource management in wireless sensor networks, ad hoc net-works, and cognitive radio networks.

KAI-TENFENG(ktfeng@mail.nctu.edu.tw) received his B.S. degree from National Taiwan University, Taipei, in 1992, his M.S. degree from the University of Michigan, Ann Arbor, in 1996, and his Ph.D. degree from the University of California, Berkeley, in 2000. Since August 2007 he has been with the Department of Electrical Engineering, National Chiao Tung University as an associate professor. He was an assistant professor with the same department between February 2003 and July 2007. He joined the Department of Electrical and Computer Engineering, Uni-versity of California at Davis as a visiting professor between July 2009 and March 2010. He was with the OnStar Corp., a subsidiary of General Motors Corp., as an in-vehicle development manager senior technologist between 2000 and 2003, working on the design of future telematics plat-forms and in-vehicle networks. His current research inter-ests include cooperative and cognitive networks, mobile ad hoc and sensor networks, embedded system design, wire-less location technologies, and intelligent transportation systemsa. He received the Best Paper Award from the IEEE Vehicular Technology Conference Spring 2006, which ranked his paper first among the 615 accepted papers. He is also the recipient of the Outstanding Young Electrical Engineer Award in 2007 from the Chinese Institute of Elec-trical Engineering (CIEE). He has served on the Technical Program Committees of VTC, ICC, and WCNC.